Euclid CollaborationInternational audienceGalaxy cluster counts in bins of mass and redshift have been shown to be a competitive probe to test cosmological models. This method requires an efficient blind detection of clusters from surveys with a well-known selection function and robust mass estimates, which is particularly challenging at high redshift. The Euclid wide survey will cover 15 000 deg2 of the sky, avoiding contamination by light from our Galaxy and our solar system in the optical and near-infrared bands, down to magnitude 24 in the H-band. The resulting data will make it possible to detect a large number of galaxy clusters spanning a wide-range of masses up to redshift ∼2 and possibly higher. This paper presents the final result...